Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8488)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8488.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(9/4)}, z] == -(((4 z (10833559295068125 - 1604971747417500 z + 531115277616000 z^2 - 631854013824000 z^3 - 415191888691200 z^4 - 127375500902400 z^5 - 55332726374400 z^6 + 10475987271680 z^7 - 316753838080 z^8 + 2147483648 z^9) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (32500677885204375 + 1375690069215000 z + 354629233728000 z^2 - 480397889664000 z^3 - 253974616473600 z^4 - 73855873843200 z^5 - 24646149734400 z^6 + 5140811612160 z^7 - 157705830400 z^8 + 1073741824 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (97502033655613125 + 22698886142047500 z + 885226653234000 z^2 - 1205878943808000 z^3 + 3108317383987200 z^4 + 1818251388518400 z^5 + 550638216806400 z^6 + 211334033571840 z^7 - 41590550691840 z^8 + 1264867868672 z^9 - 8589934592 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1386032899680000 Sqrt[2] z^(15/4)))

Standard Form

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MathML Form

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<ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]